Geodesic
On innerness of derivations on $\mathcal{S(H)}$
Lobachevskii journal of mathematics, Tome 18 (2005), pp. 21-32.

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We consider general bounded derivations on the Banach algebra of Hilbert–Schmidt operators on an underlying complex infinite dimensional separable Hilbert space $\mathcal H$. Their structure is described by means of unique infinite matrices. Certain classes of derivations are identified together in such a way that they correspond to a unique matrix derivation. In particular, Hadamard derivations, the action of general derivations on Hilbert–Schmidt and nuclear operators and questions about innerness are considered.
Keywords: Hilbert–Schmidt and nuclear operator, Nearly-inner matrices, Hadamard products. 
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A. L. Barrenechea; C. C. Peña. On innerness of derivations on $\mathcal{S(H)}$. Lobachevskii journal of mathematics, Tome 18 (2005), pp. 21-32. http://geodesic.mathdoc.fr/item/LJM_2005_18_a1/

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